One-dimensional linear transformations and filters for electronic signals are commonly employed in communications systems. There is presently an interest in applying two-dimensional linear transformations and filters to optical systems, such as television. The usual approach is to scan the image with an image sensor and then to apply the transformation or filter to the resulting electronic signals. However, if a two-dimensional transformation or filter is required, then the individual lines of the image must first be processed one at a time, the intermediate computation stored in a memory which is read out in transposed order and then the transposed signal is further processed, a column at a time, to achieve the final two-dimensional transformation. Unfortunately, the size of the memory necessary to store the intermediate computations for this two-step processing exceeds a quarter million words for a single monochrome television image. Thus, many applications of two-dimensional filtering cannot be applied in real time because of the lack of the transpose memory required for the intermediate computations.